We use charge sensing of Pauli blockade (including spin and isospin) in a two-electron \(^{13}C\) nanotube double quantum dot to measure relaxation and dephasing times. The relaxation time \(T_1\) first decreases with a parallel magnetic field and then goes through a minimum in a field of \(1.4 T\). We attribute both results to the spin-orbit-modified electronic spectrum of carbon nanotubes, which at high field enhances relaxation due to bending-mode phonons. The inhomogeneous dephasing time \(T_2^*\) is consistent with previous data on hyperfine coupling strength in \(^{13}C\) nanotubes.